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19
votes
4answers
2k views

Does mean-variance portfolio optimization provide a real edge to those who use it?

Mean-variance optimization (MVO) is a 50+ year concept, and perhaps the first seminal idea of quantitative finance. Still, as far as I know, less than 25% of AUM in the US is quantitatively managed. ...
18
votes
5answers
3k views

What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?

One of the main problems when trying to apply mean-variance portfolio optimization in practice is its high input sensitivity. As can be seen in (Chopra, 1993) using historical values to estimate ...
10
votes
1answer
421 views

Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
7
votes
0answers
805 views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed $...
6
votes
2answers
2k views

Comparing MVO with Resampled Efficient Frontier

My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
6
votes
5answers
2k views

Fastest solver possible for portfolio optimization

I am using quadprog in MATLAB for very simple mean-variance optimization, with less than 100 assets. It is quite fast but if I run a strategy with daily ...
5
votes
1answer
456 views

Robust-Bayesian optimization in Markowitz framework

Suppose we are in the mean-variance optimization setting with a vector of returns $\alpha$ and a vector of portfolio weights $\omega$. In a robust setting, the returns are assumed to lie in some ...
5
votes
0answers
305 views

Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
4
votes
3answers
2k views

Markowitz mean-variance optimization as “error maximization”

I hear it said a lot that standard MV optimization "maximizes errors". But I can't find a good explanation for what exactly they mean by this "maximization" of estimation error. I understand that if ...
4
votes
2answers
5k views

Typical risk aversion parameter value for mean-variance optimization?

What are typical values for risk aversion parameters $\lambda$ used in mean-variance optimization? Please provide references. Just to be clear, I'm talking about the $\lambda$ in $U(w) = w'\mu - \...
4
votes
1answer
546 views

Mean-variance portfolio & quadratic programming

I am somewhat confused when it comes to modern portfolio theory, mean-variance portfolio optimization and its quadratic programming formulation. Issue 1: Formulation of mean-variance portfolio ...
4
votes
1answer
94 views

Monte Carlo based mean variance optimization

I was asked this question in an interview some years ago. It struck me as a poorly formed question. I thought I would put it out there to the community to see if I just simply missed something. ...
4
votes
1answer
101 views

Calculate mean variance portfolio

I am trying to calculate the mean variance portfolio using the plug-in approach. First I generate some artificial data: x <- replicate(10,rnorm(1000)) Then I ...
4
votes
1answer
2k views

Michaud's Resampled Efficient Frontier - Out of Sample Simulation Testing

I will be putting ALL my account points on bounty to whoever answers this question [if your answer is crap but it's the only answer, you're getting the 165 points]. You will have to wait 2 days or so ...
4
votes
1answer
156 views

Matlab Portfolio Optimization with bid ask spread

I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ...
4
votes
3answers
20k views

How to calculate expected return based on historical data for Mean Variance Analysis

I've recently started reading some books on asset allocation and portfolio theory but I don't work in the field and don't have much knowledge yet. So I've been reading up on mean-variance analysis ...
4
votes
2answers
87 views

Realized “efficient” frontier. Is this reasonable?

I have performed some out-of-sample analysis of mean-variance optimization with monthly rebalancing. Studying the "realized efficient frontier", I am worried that something is wrong. Since the ...
3
votes
3answers
9k views

Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?

I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ ...
3
votes
1answer
55 views

Dollar-Neutral in addition to Market-Neutral?

What is the point/benefit of using a dollar-neutral strategy in addition to a Beta-neutral strategy? What exactly does a dollar-neutral strategy buy the investor? What's useful about balancing long ...
3
votes
1answer
195 views

Markowitz Mean-Variance Implied Returns

What is the closed form solution for the following inverse Markowitz problem? Given a mean-variance optimized fully invested portfolio $X$, a risk aversion parameter $\lambda$ and a var-covar ...
3
votes
1answer
193 views

formulating MVO with costs

I am trying to formulate this simple MVO utility function with a linear transaction cost penalty added using Quadprog in MATLAB tcost = 0.001; lambda = 4; mu = vector of expected returns (say 4x1) S ...
3
votes
0answers
38 views

Relation between mean and variance of a portfolio in modern portfolio theory:

I hope that this is the right place to ask my question! Let a market with $N\ge1$ risky assets and denote by $(R_i,i=1,\cdots, N)$ their returns and $R$ the vector of these $N$ returns. In addition, ...
3
votes
0answers
58 views

Finding mean vector and covariance matrix for annual returns given quarterly returns

I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ...
2
votes
1answer
36 views

Can the differential operator be removed to get the mean/variance of an Ito process?

If $X_t$ is an Ito process, such that: $dX_t = \mu(t, X_t)dt + \sigma(t, Xt)dW_t$ where $W_t$ is a standard brownian motion. Then we can say that: $E(dX_t) = \mu(t, X_t)dt$ and that $Var(dX_t) = \...
2
votes
2answers
93 views

How to perform portfolio optimization with user-defined expected return and variances using R?

I found some functions for Markowitz mean variance portfolio optimization in R such as portfolio.optim in tseries package. ...
2
votes
2answers
101 views

Mean Variance Portfolio theory and real-world problem?

There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example 1) investors have the same information at the same time: calculating expected returns ...
2
votes
1answer
279 views

What are the assumptions of portfolio optimisation with higher moments?

I was wondering whether there are a set of assumptions for portfolio optimisation with higher moments (including kurtosis and skewness) as there are for regular mean-variance optimisation?
2
votes
1answer
480 views

Unsystematic and systematic risk of a portfolio

I have 8 country stock indexes and 1 world stock index. I do not actually have time series data but I'm given the following data: $\mu$, the vector of expected future returns for all 8 country ...
2
votes
1answer
32 views

Are financial returns considered more volatile in recessionary times as opposed to expansionary times?

I need help in understanding some results that I have obtained. I am doing some out-of-sample performance analysis for different targets of volatility in mean-variance optimization where I solely ...
2
votes
1answer
136 views

How do I show that there is no tangency portfolio?

Question: Suppose that the risk-free return is equal to the expected return of the global minimum variance portfolio. Show that there is no tangency portfolio. A hint for the question states: Show ...
2
votes
1answer
91 views

Critical Appraisal of Approaches countering Parameter Uncertainty in Portfolio Optimization

It is very hard to come up with legit and solid advantages and drawbacks of the various approaches wich are trying to counteract parameter uncertainty in portfolio optimization procedures. In my ...
2
votes
1answer
135 views

Why does my posterior mean differs from Idzorek's results?

I have implemented two different expressions (Idzorek p.6, Walters p.51) of a posterior mean return calculation within a Black-Litterman framework. My results are the same, irrespective of the ...
1
vote
3answers
353 views

Finding Expression for Optimal Markowitz Weights

So there are two assets with return rates $r_1$ and $r_2$ which have identical variances and a correlation coefficient $p$. The risk free rate is $r_f$. I need to find an expression for the optimal ...
1
vote
2answers
1k views

Covariance of a GMV portfolio with any asset

Why is that the covariance of a global minimum variance (GMV) portfolio in the efficient frontier with any asset is always the same?
1
vote
1answer
118 views

What is the smart way to reallocate money?

We are running a portfolio of fund managers in our fund. When one of the managers hits the max DD constraint we pull money from this manager. This may happen in the middle of the allocation period and ...
1
vote
1answer
29 views

Are Variances generally stable for any given instrument?

My hesitation, as I look at getting into forecasting based on observed variances, is the nagging question - if variances are not constant per-instrument, is it any good to use the last month or year's ...
1
vote
1answer
436 views
1
vote
0answers
22 views

Should the number of Markowitz Optimization steps be counted as backtest trials?

I'm backtesting a strategy that involves monthly investments in a few stocks out of a given set, that is, each month some of the stocks are shortlisted from an index and a long position is taken in ...
1
vote
0answers
37 views

Minimum Variance Portfolio problem [closed]

Minimum Variance Portfolio Suppose there are N stocks in the investmentable universe and we have a fully invested portfolio investing 100% of the capital. The Covariance matrix is denoted as ∑. We ...
1
vote
0answers
49 views

Modelling log-returns and calculating the portfolio return

I know this might be a trivial question, however, I would be grateful for some clarification. I am working on weekly log-return data, doing volatility-foracasting using GARCH models and then using ...
1
vote
0answers
1k views

Calculating the efficient frontier from expected returns and SD

I'm trying to calculate the efficient frontier (and the optimal portfolio at the Sharpe ratio) given two vectors for a portfolio: (1) expected returns and (2) historical standard deviations. I would ...
1
vote
0answers
73 views

Transform MPT optimization problem

I am trying to teach myself about MPT and optimization. I understand that MPT solutions can be found using three equivalent optimization problems: Minimizing variance for given return limit ...
0
votes
2answers
137 views

Mean Variance Analysis: what does the solution of the following exercise tells me?

I'm new in here and I hope this is the right board to ask this question. I'm at second year of university and in the Informatics II course the lecturer made us solve the following mean variance ...
0
votes
0answers
28 views

What is the importance behind an efficient frontier to be a straight line in the standard deviation-mean plane for Mean-Variance Portfolio Selection?

I'm currently working on a research project regarding Continuous-Time Mean-Variance Portfolio Selection problem. I got curious on why is it important for the efficient frontier to be a straight line ...
0
votes
0answers
15 views

How to set the mean matrix in fPortfolio package in R

I'm doing a mean-variance analysis of 5 ETF's and insted of using the sample mean i used a time series model to forecast it. I want to do a backtest of a tangency portfolio getting the weights with ...
0
votes
0answers
55 views

Mean- variance portfolio problem

So the question asks: Consider three uncorrelated stocks in the market. Each stock has variance 1. The expected returns are given by $2, 3 $ and $ 5$ respectively. Find the optimal mean-variance ...
0
votes
0answers
60 views

Stats and Hedge Ratio calculation questions

I did self-study and learnt some concepts to build a multiple leg spread /portfolio for trading but still confuse in some basic concepts. I will be very thankful if you can answer my couple of ...